Question

PROBLEMS. Answer the following questions by justifying your answer. Show work where applicable.

19. The period, T, of a pendulum is the time it takes for a pendulum to swing back and forth once. If the dimensional quantities that a period have depend on gravity, g, and the length of the pendulum, write an equation for T expressed in terms of the fundamental properties of g and L.

20. Given h/mv = λ , determine the wavelength of an electron with a velocity of 6.0 x 106 m/s, if m= 9x10^-31 kg, and h= 6x10^-34 Jxs.

Answer 1

We know that, the period (T) of a pendulum is the time which taken for a pendulum to swing back and forth once.

(i) An equations for a period expressed in terms of the fundamental properties of 'g' and 'L' which will be given as -

T = 2L / g

where, L = length of the pendulum and g = acceleration due to gravity

(ii) The wavelength of an electron which will be given by -

= h / m v

where, h = planck's constant = 6 x 10^-34 J.s

m = mass of an electron = 9 x 10^-31 kg

v = speed of an electron = 6 x 10⁶ m/s

then, we get

= (6 x 10^-34 J.s) / [(9 x 10^-31 kg) (6 x 10⁶ m/s)]

= [(6 x 10^-34 J.s) / (5.4 x 10^-24 kg.m/s)]

= 1.11 x 10^-10 m

converting m into nm :

= 0.111 nm